# pgfDpoissonpascal: Function pgfDpoissonpascal. In Compounding: Computing Continuous Distributions

## Description

This function calculates value of the pgf's first derivative of the Poisson-Pascal distribution.

## Usage

 `1` ```pgfDpoissonpascal(s, params) ```

## Arguments

 `s` Value of the parameter of the pgf. It should be from interval [-1,1]. In the opposite pgf diverges. `params` List of the parameters of the Poisson-Pascal distribution, such that params<-c(theta,p,k), where all parameters are positive.

## Author(s)

S. Nadarajah, B. V. Popovic, M. M. Ristic

## References

Johnson N, Kotz S, Kemp A (1992) Univariate Discrete Distributions, John Wiley and Sons, New York

http://www.am.qub.ac.uk/users/g.gribakin/sor/Chap3.pdf

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24``` ```params<-c(5,.4,.3) pgfDpoissonpascal(.5,params) ## The function is currently defined as pgfDpoissonpascal <- function(s,params) { m<-s[abs(s)>1] if (length(m)>0) warning("At least one element of the vector s are out of interval [-1,1]") if (length(params)<3) stop("At least one value in params is missing") if (length(params)>3) stop("The length of params is 3") theta<-params[1] p<-params[2] k<-params[3] if (theta<=0) stop ("Parameter theta must be positive") if (p<=0) stop ("Parameter lambda must be positive") if (k<=0) stop ("Parameter k must be positive") theta*k*p*(1+p-p*s)^(-k-1)*exp(theta*((1+p-p*s)^(-k)-1)) } ```

Compounding documentation built on May 2, 2019, 1:04 p.m.